Craft navigating apparatus



Jan. 5, 1937.

A. L. Ruiz CRAFT NAVIGATING APPARATUS Filed May 16, 193e 2 Sheets-Sheet 2 Inventor: Albert L. Ruiz b5 fmfww.

Patented Jim. s, 1937 UNITED STATES CRAFT NAVIGATING APPARATUS Albert L. Ruiz, Schenectady, N. Y., assigner to General Electric Company, a corporation of New York Application May 16, 1936, serial 10.80.099

11 Claims.

plurality of radio transmitters arranged laterally l of the course and at known distances from the course measured on the line joining the transmitters, the angle between the line and the course also being known. 'I'he craft carries radioreceiving apparatus including directive antennae each arranged to be responsive to the waves from one transmitter and to be maintained oriented with respectthereto. In that application, it is shown that as long as the craft is on the course the relation of the said known quantities and the angles between the course and the lines joining the craft with the transmitters may be expressed by a trigonometric equation of which one side is zero.

One object of my invention is to provide improved apparatus to be carried by the craft for continuously solving such` an equation whereby an indication may be given to the pilot when the craft is on the course or how much deviation may have occurred and whereby the craft may be steered automatically to keep it on the course.

Another object of my inventionvis the provision of improved apparatus for giving various other vindications of assistance to the pilot in the navigation of the craft, such as the distance traversed by the craft, the speed thereof, the direction of the wind and the wind velocity.

My invention will be bet-ter. understood from the following description taken in connection with the accompanying drawings, and its scope will be pointed out in the appended claims.

In the drawings Fig. l is a diagram showing one 'relative arrangement of the course, the sources of radiant energy, and the craft, Figs. 2A a'nd 2B which belong together show one form of apparatus illustrating my invention and Fig. 3 is a velocity diagram. I

In Fig. 1 I have representedthe craft, such as the airplane at I, which it is desired to have travel on a straight course represented `by the line D, which line makes the angle J with the magnetic north, the direction of the wind being represented by an arrow. At opposite sides of the course D and at the points A and B are two sources ofradiant energy, such, for example, as radio transmitters which are represented diagrammatically at 2 and 3respective1y, which (Cl. 'i3-151) transmitters operate on different frequencies. 'I'he line# connecting the two transmitters intersects the course D at the point o and makes an angle with the course D which is known and which is represented by C. The distances between the points A and B occupied by the transmitters and the course as measured on theA connecting line 4 are known and are represented respectively by m and n. A',I'he constantly varying angles between the course and the lines connecting the craft with the points A and B are represented by M and N respectively.

In the aforesaid application, it is shown that as long as the craft remains on the course D the sum of distances m and n times the cotangent of the angle C minus the distance m times the cotangent of the angle M plus the distance n times the cotangent of the angle N equals zero.

Expressed in the form of an equation this relation is as follows:

(man cot c-m cot M+n not N=o (1)' In the same application it is shown also that the distance, represented by D, travelled by the craft is equal to m times the sine of angle C minus' the angle M divided by the sine of angle M which expressed in the form of an equation is:

m sin (C-M) W 2) Since the sine andthe cosecant are reciprocals Equation (2) obviously may be written thus:

D=m sin (C-M) cosec M (3) From the above Equation 1) it will be seen that for every point Y occupied by the craft on the line D the equation is satisfied; hence if the values if the craft deviates to the other side of the course,

the left side of the equation will equal some negative quantity dependent upon the amount of the deviation.

I shall now describe apparatus vwhich I have devised for` continuously solving the above equations, which apparatus is provided with means for initially setting into it the known quantities and for continually feeding into it the variable quantities. The apparatus is provided with an indicatorby which the pilot may observe when the equation is satised and if not satisfied whether the craft has deviated, due to drift or other causes, to the right or to the left of the course. I have shown the apparatus including means for automatically steering the craft so as to cause it to travel on the straight course thereby compensating for drift or other factors which may cause it to deviate therefrom. I have also provided means for indicating the distance travelled by the craft, the speed of travel of the craft, the direction of the wind, and the wind velocity.

The craft I, see Fig. 1, is provided with a plurality of radio receivers each tuned to the frequency of one of the two transmitters 2 and 3 and each provided with a directive receptor having means whereby it is automatically maintained oriented with respect to the transmitter to the frequency of which the corresponding receiver is tuned. Thesedirective receptors lare represented as antennae in the form of the loops 5 and 6, loop 5 being maintained oriented with respect to the transmitter 2 at the point A in response to energy received therefrom and loop 6 being maintained oriented with respect to the transmitter 3 at the point B, likewise ln response to energy received from the latter transmitter. As noted above, the angle between the course and the line AY is represented by M; likewise the angle between the course and the line BY is represented by the angle N. It will be understood that as the craft travels on its course and the angles M and N continually change, the angles made by the loops `5 and 6 also continually change, the angles of the loops 5 and 6 serving as a measure of the angles M and N respectively.

The craft also is provided with a compass such for example as a magneto compass represented at 8 in Fig. 2A and this compass is provided with suitable means such as that disclosed in the Becker Patent 1,991,443 February 14, 1935, for maintaining the pole pieces thereof in an east and west position in response to the voltage produced in the armature when the pole pieces are deflected from that position. This apparatus is represented in its entirety by the 'rectangle 9 which connects through the gearing I0 and the shaft II with the pole piece mounting of the compass. The means by which the loops 5 and 6 are maintained oriented with respect to the transmitters 2 and 3 respectively are like that disclosed in the abovementioned patent for steering the craft and such means are represented respectively by the rectangles I2 and I3. These means, it will be understood, operate directly on the shafts carrying loops 5 and 6 in place of the cord and pulley 50 of the aforesaid patent.

I shall now describe specifically one form of apparatus which I have devised into which the above-mentioned known fixed quantities may be initially set and into which the changing quantities may be continuously fed, which apparatus may be used for continuously solving Equation 1. I shall also describe a form of apparatus for automatically effecting the steering of the craft to maintain it on the course in accordance with the solving of that equation.

The apparatus comprises in part three similar mechanisms I, II and III constructed and connected to compute the first, second, and third terms respectively of Equation (1). The respective mechanisms include slotted pivoted arms I6, I6' and I6" having at their outer ends thegear segments I'I, I1' and I'I" by which the arms are rotated, these gear segments being in mesh with pinions I8, I8' and I8". Intersecting the arms are the slotted horizontal slides I9, I8' and I9" which are arranged to move in a vertical direction only and which are threaded on the screws y 20, 20' and 20" by which they are moved. Also intersecting with the arms are the slotted vertical slides 2|, 2I and 2l" which are arranged to move in a horizontal direction only and which have portions forming racks 22, 22 and 22" which engage the gears 23, 23' and 23". The arm and the two-slides are caused to intersect at a common point by the pins 24, 24 and 24". It will be seen that with this construction if an arm is moved to a given position and the horizontal slide is moved to a given position, the vertical slide must assume a position which is a function of the positions of the other two members.

'I'he known angle C is initially set into the mechanism I by rotating the crank 26 which connects through the gearing 21 with the gear I8 and with the angle indicator 28 until the desired angle is shown by the indicator. The arm I6 of mechanism I is thereby set at the desired angle C.

The distance m is set into mechanism I by rotating the crank 30 which connects through the gearing 3I with the indicator 32 and through the differential gear 33 with the shaft 2li. The resulting rotation of the screw 20 moves the slide I9 to a position in accordance with the movement of the crank 30 as indicated by the indicator 82. Distance n is also set into the mechanism by rotating the crank 35 which through the gearing 36 operates the indicator 31 and through the shaft 38, the spur gearing 39 and the differential gear 33 also turns the screw 20 in the same direction as before so as to move the slide I8 an additional amount in accordance with the distance n, as indicated by the indicator 31. It will be readily seen that since the position of the arm I6 represents the angle C and the position of the slide I8 represents the distance m plus n, the position of the slide 2l will represent the product of m plus n and the cotangent of the angle C. 'I'hus the resulting movement of the gear 23 is proportional to. (ms-n) cot C which is the rst term of Equation (1).

Referring now to mechanism II, the loop 5 will have been moved by the orienting means I2 through the angle between the craft axis and the line connecting the craft with the point A. Through the operation of the magneto compass 8 the angle of the craft axis with respect to north is added to the above-mentioned angle by means of `the differential gear 40, the sum being Vequal to the angle M'. By turning the crank 44 the proper amount as shown by the indicator the magnetic bearing of the course, namely angle J, is set into the mechanism. This angle J is subtracted from angle M by the differential gear 4I the difference M-J which is the same as 180-M being transmitted to segment Il' through the shaft 42, clutch 43, and pinion I8'. Thus the angle of arm I6 is equal to 180-M.

The distance m is set into mechanism II through the shaft 41 which through the gearing 48 rotates the screw 20', to move the slide I9. Since the angle of the arm I6 is equal to 180'M and the position of the slide I9 represents the distance m, the position of the slide 2 I will represent the product of m and the minus cotangent of M. Thus the resulting movement of the gear 23 is proportional to -m cot M which is the second term of Equation (1).

Referring now to mechanism III the loop 6 will be moved by the orienting means I3 through the angle between the craft axis and the line connecting the craft with the point B. Through the operation of the magneto compass 8 the angle of the craft axis with respect to north is subtracted from the above-mentioned angle by means of the differential gear 50, the diii'erencebelng equal to the angle N'. c

The magnetic bearing of the course having already been set in the apparatus by turning the crank Il, the angle J is added to the angle N' by the differential gear 5|, the sumvNf-l-J `which is the same as 180-N being transmitted to segment I1" through the shaft 52, clutch 53 and pinion |8". Thus the angle of the arm I6" is equal to 180-N. The distance n is set into mechanism III through the shaft 5I which through the gearing 55r rotates the screw 28."l to move the slide I9". Since the angle oi' the arm I6" is equal to 180-N and the position of the slide |9" represents the distance n, the position of the slide 2|" will represent the product of n and the minus cotangent of N. Thus the resulting movement of the gear 23" is proportional to n.cot N which is the negative of the third term y is transmitted through the gearing 60' to the dial 6| of the course indicator having the fixedv pointer 62. If the craft is on the course the` zero mark of the'dialiil will stand opposite the pointer 62 and .thus indicate to the pilot that the craft yis travelling on the course. If, on the other hand.

, the zero mark is at either side of the pointer, the

pilot knows that the crafthas deviated from the course, the l direction and the amount of the deviation being indicated by the dial. l With that information he-may-turn the` rudder to bring the craft back on the course. l Y

The craft maybe steered automatically 'to keep it onthe course by controlling the `rudderin accordance with the angular positionA of the dial 6|.

The means which I have illustrated for so moving the. rudder is to a certainuextentlike that disclosed in .the above-mentioned vPatent 1,991,443. In the present'case the rudder 65 is connected by the cables 66 with the gearftlgwhich is arranged to beV moved in one`dlrection', or the other from the 'midposition,.illustrated by the lreversible motor lill. The 4direction of rotation of this motor vis controlled bytherelay 69r having the' two windings 1 0 and 1| which are connected to be" energized by the battery 12 under the control of the discharge devices 18 gand 14 respectively. These devices in turn are controlled by the polarized relay 15 in a,l manner similar to that of the polarized relay 20 and discharge devices 2| and 22 of the above-mentioned patent. The winding of the polarized relay 15 is arranged to be energized by current in one Idirection or the other in accordance withl the .position ,of the contact 16 secured tb the scale '6| vand arranged to move over the vresistor 11: This` resistor has its' ends co'nnected with the ends of a similar resistor. 18 and with the 'ends ofthe*l battery 19. The contact-80 carriedv vby. the gearV 61' and connected' with the winding :of the polarized relay engages the re` x tact 16 suppliescurrent in. a direction to energize relay 15 whichfthrough one or 'the 'other of .the

a craft. Y vmunicated"through gearing such as |05, and shaft calibrated to read in miles.

discharge tubes energizes the relay 69 in a direction to cause the motor to turn the gear 81 so as to change the position ot the rudder to correct the deviation. The rheostat 18 and contact 80 constitutes. follow up arrangement whereby the operation of the motor 68 operates to turn the craft through successive increments until it has' reached the final position in the same manner and for the same purpose as described in the aforementioned patent.

.slot 8l therein forming a cosecant cam. The

gear lis connected through the shaft 88 and gears thereon with the crank 26'associated with theindicator of angle C whereby when angle C is set into the apparatus the gear and cosecant cam is rotated through an angle equal to C. Mounted concentrically with the gear is the outer gearI 89 which has the slotted radial arm 90. This gear 89 is rotated in the same direction as the inner gear through an angle equal to the angle C minus the angle M by means of the differential gear 9 since by this differential gear and the spur gearing 92 the movement of the shaft 42 is subtracted from that of shaft 88. 'I'his differential movement is transmitted through the gearing 93 to the outer gear 89. The relative movement between the inner and outer gears is C-(C-M) which. equals M. Arranged for vertical movement between two suitable guide surfaces is the slotted horizontal bar 95 and this bar, the arm 90 and the face of the cosecant cam are caused to intersect at a common point by the pin 96. In-A asrnuch as the vrelative movement" between gears 85 and 89 is proportional to angle M, the distance between pins 96 andr86 is equal to the coseca'nt of v M. Also since the gear 89 has been moved through angle C -M the vertical displacement of the pin 96 and hence of the bar 95 is equal to sin (C-M) csc M. l y

Bar 95 being common to mechanisms IV and V, the vertical movement of this bar is communicated to mechanism V. In'this mechanism the slotted link 98 is pivoted to the fixed pivot 99 adjacent one ende-nd at the opposite end is pivoted to the nut |00 which is threaded on the screw |0|. This screw connects through the gearing |02 with' the screw 20' of mechanism II. By this means the distance m is transmitted to the upper end of the link 98. The slide |03 which is similar to slide `2|, intersects the bar 95 and the link 98, the pin |04 causing the three members to intersect at va common point. By the mechanism Vthe vertical displacement of the bar 95 is combined with the quantity m whereby the horizontal V.displacement of the slide |03 is equal to m sin (C-M)csc M whichl according to Equation (3) equals the distance traversed by the Movement of theslide |03 may be com- |06 to the odometer |01 which, ifdesired, may be Inasmuch as the loops 5` and 6 do By means of the ap-A paratus thus described the craft may be steered not necesslide |03 accordingly may be intermittent.

sarily follow the changing positions of the transmitters 2 and 3 to which they are responsive with steady movements but may follow them rather by series of small increments, the movement of the The average rate of movement of the slide |03 is a measure of the speed of the craft and in order that I may employ a speedometer of a common form, such for example as that shown at |08, Fig. 2B, for indicating the speed of the craft, suitable means are provided for reducing the intermittent motion to a steady movement. Such means I have represented as comprising a well known form of over-running clutch |09 between which and the speedometer is the flywheel ||0.

If the course to be travelled is such that it passes through one of the transmitters, 'forexample, the transmitter 3 at the point B, then the angle N will be zero as long as the craft is on the course. In this case for course indication and automatic steering transmitter 2 and the receiver including loop 5 are not necessary, hence clutches 43 and 53 should be disconnected and quantity n should be set at zero. The clutch ||2 will be closed thereby establishing a direct connection between the shaft 52 and the indicator through the shaft ||3 and gearing ||4, the mechanisms II and III now being inoperative. Thus any change in angle of loop 6 resulting from a deviation of the craft from the course will be indicated by the indicator 6| as before. The distance travelled and the speed of the craft are obtained by mechanisms IV and V as a result of the changing angle M in the manner' already described above.

I shall now describe the apparatus which I have devised for indicating to the pilot the direction and the velocity of the wind. Referring to Fig. 3 the length of the line W represents the speed of the wind relative to the ground, the length of the line G represents the speed of the craft relative to the ground, the length of the line S represents the speed of the craft relative to the wind, w is the angle between 'S and G, and X is the angle between G and minus W. From the triangle thus formed it is evident that W may be expressed as follows:

W=G cos J-S cos(w-X) (4) And also X may be expressed as follows:

S X arctangentlv (5) The angle w, which is the angle of crab of the craft, is obtained by subtracting the angle of the course relative to the north-south magnetic line from the angle of the axis of the craft relative to that line. This is done by means of the differential gear ||6 the lower portion ofl which is connected by the spur gearing ||1 with the lower portion of differential gear 5| which in turn is 4connected with the crank 44 by which the magnetic bearing of the course was set into the apparatus. The upper part of differential gear ||6 connects through the spur gearing ||8 with the lower portion of differential gear 50 and hence with magneto compass 8. The resulting movement of the shaft ||9 equals the angle w or angle of crab of the craft.

Referring now to Fig. 2B the mechanism VI comprises the two concentrically mounted ring gears |20 and |2|, the former being geared directly to shaft ||9 and the latter being geared to the same'shaft ||9 thgough the differential gear |22. The gearing by which the two ring gears slide |26 mounted for horizontal movement only and provided with a vertical slot for receiving the pin |21 carried by the screw |24. Also cooperating with the ring gears is the bar |28 which is mounted for vertical movement only in a manner similar to that of bar 95 previously described. This bar has a horizontal slot which also receives the pin |21. Through the differential gear |22 movement is also transmitted to the inner ring gear |2| in accordance with the velocity of the wind with respect to the craft. Any well known form of apparatus for producing this movement may be employed. I have illustrated a simple form of apparatus for this purpose as comprising the closed air chamber |30 from which extend tubes |3| and |32. The former tube is closed at its outer end and is provided with a series of openings |33 in the side thereof. Tube |32 is open at its outer end and at the inner end connects with one end of the bellows |34 the opposite end of which connects with the crank |35 on the shaft |36. The angular position of this shaft, therefore, is responsive to the speed of the Wind relative to the craft and is represented by the indicator |31. In order that the movement of shaft |36 may be employed to rotate the ring gear |2| as well as other parts of the mechanism, I employ suitable motor driven mechanism to supply the necessary power under the control of this shaft. Such a mechanism is represented as comprising the reversible motor |38 which serves to turn the gear |39 in one direction or the other under the control of shaft |36. The gear carries two spaced xed contacts |40 and the shaft carries a cooperating movable contact |4l, the contacts serving to control the direction of rotation of the motor |38 through the relay |42 in the well understood manner. By this mechanism the angular position of the shaft |43 is responsive to the velocity of thecraft relative to the air. Through the differential gear I22, therefore, the ring gear |2| is moved relative to the outer ring gear |20 an amount proportional to the velocity of the craft relative to the wind. Hence the position of the pin |21 with respect to the center of the ring gears is proportional to the velocity of the craft relative to the wind which is the quantity S in Fig. 3. The horizontal displacement of the slide |26 hence is equalto S times the cosine of w and likewise the vertical displacement of the bar |28 is equal to S times the sine of w. Before combining the movement of the bar |28 with the.movement of the slide |26 by means of the mechanism VII in orderl to obtain the direction of the wind it is necessary to subtract from vthe movement of slide |26 the quantity G which to the speed of the air passing the craft. It in- 75 cludes the reversible motor |44 controlled by the relay |48 which in turn is controlled by contacts on the gear |48 and the cooperating contact |41 on the shaft |48 of the speedometer. Movement of the shaft |48 which is geared to the gear |48 the horizontal displacement of the slide |88 or I t S coo wg- G From Equation (5) it will be seen that the angular displacement of arm |84 equals the arc tangent of the above quantity which equals the angle X. Movement of arm |84 is transmitted through the shaft |81 to the indicator |58 whichV indicates the angle X which is vthe direction of the wind.

'Ihe mechanisms VIII and IX by means of which vthe velocity of the wind is indicated are similar to mechanism VI in that they include respectively outer ring gears |88 and |80', inner ring gears |8| and I8|', yokes |82 and |82'carried by the outer ring gears. screws |88 and |83' mounted in the yokes and having threaded thereon gear nuts |84 and |84'. and horizontally movable slides |88 and |88' having slots engaged by pins |88 and |88' carried by the screws. Shaft |68 being geared to shaft ||9 turns in accordance lwith the angle w; likewise shaft |88 being geared to shaft |81 turns in accordance with the angle X. 'I'hrough the dierential gear |10 movement of the shaft |88 is subtracted from that of shaft |88 whereby movement of shaft |1| is proportional to w-X. The movement of this shaft |1| is transmitted to both ring gears |88 and |8|y through the gearing shown and the differential gear |12 whereby both gears are rotated an equal amount due to movement of the shaft |1I. 'I'he inner ring gear |8| is` rotated an additional amount through the differential gear |12 in accordance with the movement of shaft |48; hence the radial displacement of pin |88 from the center ci the ring gears is proportional to S. `The horinontal displacement of the slide |88 therefore is proportional to S cos(w-X) In a similar manner ring gears |88' and |8i' of mechanism m are rotated in accordance with the angle X by reason of the geared connections thereto with the shaft |81. 'Ihe inner'ring gear is additionally moved and hence the pin |88' is displaced from the lcenter of the ring gears an v amount proportional 'to the movement .of shaft |48 by reason of the connection therewith including the dierential gear |18. Hence the dis-a placement of the slide |88' is proportional to G cos X. The movement of slide |88 is subtracted from the movement of |88' by means of the differential gear llt and hence the shaft |15 1s proportional to i. to i G cos X-S cos(w-X) which in accordance with Equation (4) is equal to the speed or velocity of the wind relative to theground. This value is indicated by the wind velocity-indicator |18.

movement of l In the drawings I have not attempted to show the various parts of the apparatus in their true relative proportions nor have I attempted in all cases to show the gears arranged for rotation in the proper direction or having the proper gear ratio.

I have chosen the particular embodiment described above as illustrative oi' my invention and it will be apparent that various modifications may be made without departingfrom the spirit and scope of my invention which modifications I aim to cover by the appended claims.

What I claim as new and desire to secure by Letters Patent of the United States is:

l. In a system for steering a craft on a straight course employing reference points A and B located laterally of said course on a line making an angle C with the course and at distances m and n respectively therefrom measured on said line, the direction of the points A and B from the craft making angles M and L respectively with the course. a first, atsecond. and a third mechanism all of similar construction and each including a plurality of slides at right angles to each other; a rotatable arm and' means for causing the slides and the arm to intercept'at a common point,

' means for moving corresponding slides ofthe respective mechanisms distances proportional to the` sum'of distances m and n, distance m, and distance n, means for rotating the arms of the respective mechanisms through angles equal to the angle C, the angle M and the angle L and means for summing up the resulting movements of the other slides oi the mechanisms.

2. In a system for guiding a craft on a straight -course employing a reference point A located at one side of the course and at a distance m therefrom measured on a line making an angle C therewith, the direction of the point A from the craft making an angle M with the course, a slide mounted for movement transversely of its length. means for moving the slide a distance proportional to the product of the sine of (C-M) and' the cosecant of M, a link slidably connected at one portion with a fixed pivot. means for moving another portion thereof at right angles to the movement of said slide in proportion to m. a sec- `ond slide movable at right angles to the movement oi the first slide and means for causing said slides and link to intersect at a common point, the movement of said second slide being proportional to the distance traversed by' the craft.

3. In a system for guiding a craft on a straight course employing a reference point A located at one side of the course and at a distance m therefrom measured on a line making an angle C therewith, the direction of the point A from the craft making. an angle M with the course, a slide mounted for movement transversely of its length, a cosecant cam rotatable in accordance with angle C, an arm rotatable in accordance with the difference between angles C and' M, means for causing said slide, said cam and said arm to intersect at a common point, a fixed pivot, a link slidably connected therewith, means for moving one end of the link at right angles to the movement of saidl slide in proportion to m; a second slide movable at right angles to the movement of the first slide, means for causing said slides from measured on a line making an angle C therewith, the direction of the point A from the craft making an angle M with the course, a slide mounted for movement transversely of its length, a rotatable cosecant cam, means for setting said cam in accordance with angle C, a rotatable arm,

the movement of said slide, means for setting said end in proportion to m, a second slide movable at right angles to the movement of the rst slide, means for causing said slides and link to intersect at a common point, and a speedometer connected to be driven by said second slide.

5. In a system by which a craft may be guided on a straight course, apparatus for indicating the direction of the wind when the air speed, the ground speed and the angle of crab of the craft are known comprising a plurality of slides mov'- able in directions at right angles to each other, a rotatable arm, means for causing said slides and arm to intersect at a common point, means for moving one of said slides in accordance with the product of the air speed and the sine of the angle of crab, and means for moving the other slide in accordance with the product of the air speed and the cosine of the angle of crab minus the ground speed of the craft, the resulting angular position of said arm indicating the direction of the wind relative to the course,

6. In a system by which a craft may be guided on a straight course in a known direction, apparatus for indicating the direction of the wind when the air speed andthe ground speed of the craft are known, comprising means for subtracting the angle between the axis of the craft and the north-south magnetic line from the angle between the course and said line thus giving the angle of crab of the craft, a plurality of slides movable in directions at right angles to each, a rotatable arm, means for. causing said slides and said arm to intersect at a common point, means for obtaining the product of said air speed and the sine of said angle of crab, means for moving one of said slides in accordance with said product, means for obtaining the product of said air speed and the cosine of said angle of crab, means for obtaining the difference between the latter product and said ground speed, and means for moving the other of said slides in accordance with said difference, the resulting angular position of said arm being an indication of the angle of the wind.

1. In apparatus of the character described, mechanism for obtaining the product of a. given quantity and the cosine of a given angle comprising a plurality of concentric rotatable members, a screw mounted on one of said members for longitudinal movement radially thereof, a nut on said screw carried by said one member and arranged to be' rotated by the other member, means for rotating both of said members through angles equal to said given angle and means for rotating said other member in accordance with said given quantity.

8. In a system of the character described wherein the air speed of a craft traveling on a straight course and the angle of crab are known,

means for rotating the other of said members in v accordance with said air speed, means carried by said one member and arranged to be rotated by the other member for moving said diametrical member and means for causing said slides and diametrical member to intersect at a common point, whereby the displacement of one slide is proportional to said speed times the sine of said angle of crab and the displacement of the other slide is proportional to said speed times the cosine of said angle of crab.

9. In a system of the character described wherein the air speed of a craft traveling on a straight course, the angle of crab of the craft and the ground speed of the craft are known apparatus for indicating the direction of the wind comprising a plurality of slides arranged for movements at right angles to each other, a rotatable arm, means for causing said slides and arm to intersect at a common point, means for moving one of said slides a distance proportional to the product of said air speed and the sine o! said angle and means for moving the other of said slides a distance proportional to the product of said air speed and the cosine of said angle minus said ground speed, the resulting position of said arm being an indication of the direction of the wind.

l0. In a system of the character described wherein the air speed of a craft traveling on a straight course, the angle of crab of the craft, and the ground speed of the craft are known apparatus for indicating the direction of the wind comprising a slide and a slldable bar arranged for movements at right angles to each other, a plurality of concentric rotatable members, means for rotating both members through an angie equal to said angle of crab, a screw mounted for longitudinal movement on and arranged diametrically of one of said members, means for rotating the other of said members in laccordance with said air speed, a nut'on said screw carried by said one member and arranged to be rotated by the other member, means for causing said slide, bar and screw to intersect at a common point, a second slide arranged for movement at right angles to said bar, a rotatable arm, means for causing said second slide, said bar and said arm to intersect at a common point and means for moving said second slide a distance proportional to the movement of the first mentioned slide minus said ground speed.,

11. In a system of the -character described wherein the air speed and the ground speed of a craft traveling on a straight course, the angle of crab and the angle of the wind are known, apparatus for indicating the velocity of the wind comprising means for producing the difference between the angle of crab and the angle of the wind, means for producing the product of the cosine of said difference and said air speed, means for producing the product of the ground speed and the cosine of the angle of the wind and means for subtracting the second of said products from the first product.

ALBERT L. RUIZ. 

